The two sentences are basically the same. They both can be used when asking the others to make more dishes, or when explaining why the speaker himself/herself preapares to make a lot of dishes.
But when the dishes are already cooked, and someone asks me why so many dishes are made, I'll use the first sentence, or "菜做得多了一点儿". The second sentence doesn't seem to fit in this situation
The two are basically the same in meaning. But the Chinese expression suggested by lglfa is most natural to native Chinese ears. Yours can be understood, but not very well expressed in my view. Worse, the second "今天是他的生日。做多一点儿菜，他很喜欢吃中国菜?" has a slip there: using two same characters in the end of two adjacent clauses/sentences sounds more or less awkward in native Chinese ears. It is better to avoid it.
I do NOT use "V + 得" (e.g., 做得多, 跑得快) for the imperative mood. I reserve the resultative 得 (e.g., 你跑得比他快) for descriptive sentences.
你跑快点儿 (imperative) vs. 你跑得快点儿 (descriptive)
菜多做点儿 (imperative) vs. 菜做得多点儿 (descriptive, e.g., 菜做得多点儿又不是什麼天崩地塌的大事)
多喝 "drink more" vs. 喝多 "drink too much"
多吃 "eat more" vs. 吃多 "eat too much"
多做一点儿菜 "cook a bit more" vs. 做多一点儿菜 "cook a bit too much"
今天是他生日, (所以我)菜做得多一点儿，(我知道)他愛吃中国菜 ==> The resultative 得 is used in a descriptive sentence with an implied subject "I".
今天是他生日, (你得)多做一点儿菜，(我知道)他愛吃中国菜 ==> It is an imperative sentence with an implied subject "you".
今天是他生日, (我)做多了一点儿菜，(我以為)他愛吃中国菜 ==> I cooked a little bit too much.